If I'm not mistaken, insufficient chill hours would be problematic in other ways beyond fruiting. You probably hit the nail on the head about pollination though. Pretty sure Ume needs cross-pollination, although other plums and/or apricots might work too. Finally, the majority of Ume are ornamental, and not for fruit production anyway...

I had thought ume plums, being basically an apricot, were self fertile. Edible landscape only sells 1 variety, implying its self fertile. Raintree says they're partially self fertile. But I can't find much information online about ume's so I'm not sure.

I'm getting my first ume's this year on a tree in its 4'th leaf. Another 4 year old, and a 5 year old, are not fruiting. I had always blamed the late January blooming followed by hard freeze's in feb. each tree has blossomed in their second year. Perhaps they take 4-5 years?